Local convertibility and the quantum simulation of edge states in many-body systems

Abstract

In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity is a potential indicator of non-classicality. In this work we demonstrate that such a phenomenon, known as non-local convertibility, is due to the edge state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transitions. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.

Accepted by Physical Review X. 5 pages (+ 2 pages of Methods & SupplementaryMmaterial). 11 figures. Several changes since first submission

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• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• The Magnetic Grüneisen Parameter for Model Systems
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• Frustrated quantum spin systems in small triangular lattices studied with a numerical method
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Phase diagram of quantum critical system via local convertibility of ground state
• Entanglement-fluctuation relation for bipartite pure states
• Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
• Resource complexity of Symmetry Protected Topological phases